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Yup, column shift linkage. The part you have your finger on connects to a bracket on the frame, and the other end connects to a U shaped bracket on the side of the trans to select gears.
More seriously, though, what kind of tranny do you have on that 5.3, some 4L60E sort of thing? The new-fangled ones, I donno, maybe they have an electronic prundle, and you'll need a mechano-electric-prundle adapter